Delta is not the probability, and the difference has a shape
Delta approximates the chance an option finishes in the money but consistently overstates it. The model probability is N(d2), a distinct quantity. On a 0.331 delta UBER call the true odds are 29.3 percent, and the probability that matters more than either is the 59 percent chance the stock touches your strike at all.
"Sell the 0.30 delta and you keep the premium 70 percent of the time." Repeated everywhere, roughly right, and wrong in three specific ways that are worth knowing.
The two numbers
The October 17 $72.50 call on UBER, 42 days out, stock at $68.40.
- Delta: 0.331.
- N(d2), the model's probability of finishing in the money: 0.293.
Delta overstates by 3.8 points. That is not a rounding artefact, it is structural: delta is N(d1), and d1 and d2 differ by the volatility times the square root of time. The higher the volatility and the longer the expiry, the wider the two drift apart.
Which means the error grows exactly where you might rely on it. On a 42-day contract at 32 percent volatility, 3.8 points. On a six-month contract on something at 70 percent, considerably more.
The gap across the chain
| Strike | Delta | True P(finish ITM) | Overstatement | P(touch) |
|---|---|---|---|---|
| $70 | 0.455 | 41.2% | 4.3 pts | 82% |
| $72.50 | 0.331 | 29.3% | 3.8 pts | 59% |
| $75 | 0.227 | 19.5% | 3.1 pts | 39% |
| $80 | 0.089 | 7.3% | 1.6 pts | 15% |
The gap is widest near the money and shrinks in the wings, which is a mildly reassuring shape: the strikes people actually sell are where the approximation is worst.
The direction of the error is in your favour
Worth pausing on. If you sell the 0.331 delta call and assume you keep it 66.9 percent of the time, the model says you keep it 70.7 percent of the time. Using delta as your probability is conservative for a short position.
That is the good news and it is small. The problem is not the 3.8 points. It is the third column.
The probability nobody quotes
Your $72.50 call has a 29.3 percent chance of finishing in the money. It has a 59 percent chance of touching $72.50 at some point in the next 42 days.
Roughly double, and that is not a coincidence: for an out-of-the-money strike, the probability of touch runs at about twice the probability of finishing there. The stock has 42 days of wandering to do and only the last day counts for settlement.
So the honest description of a 0.30 delta short call is: you will probably keep the premium, and you will probably watch the position go against you before you do. More than half the time, this trade gets tested.
That single number explains most bad options behaviour. People sell a "70 percent probability" trade, get tested six out of ten times, panic, roll or close at a loss, and conclude the odds were a lie. The odds were fine. Nobody told them what the path looks like.
Three reasons all of this is softer than it looks
It assumes lognormal returns. Every probability on this page comes out of the same model whose distribution has thinner tails than reality. The chance of a large adverse move is understated across the board.
It is a risk-neutral probability, not a forecast. N(d2) is the probability in a mathematical world constructed so that nobody earns a risk premium. It is not the real-world chance and it was never meant to be. For most short-dated equity work the two are close, and the distinction becomes real over long horizons.
Skew makes the put side worse. Downside strikes carry higher implied volatility, so a 0.20 delta put and a 0.20 delta call are not the same bet. The market charges more for the put because it thinks the downside is likelier than a symmetric model does, and your delta was computed by the symmetric model.
How to actually use it
- Delta as a rough keep-rate is fine. 0.30 delta, roughly 70 percent. It errs in your favour on a short.
- Double it for the path. Whatever your delta, expect to be tested at roughly twice that rate. Decide in advance what you will do when it happens, because you will need the answer.
- Treat put deltas as a floor. On the downside the model understates the tail and the market knows it.
- Never size on the probability. A 93 percent win rate on the $80 call means nothing if the 7 percent is unsurvivable. Size against the outcome, not the odds.
OptionsKing scores every candidate strike on a deterministic 0 to 100 scale, blends that score with the return on the capital the trade ties up, and shows you the highest-ranked handful. There is no minimum score. How it works covers what the ranking does and does not tell you.
Questions people actually ask
Is delta the same as probability of expiring in the money?
Close but consistently high. The model probability is N(d2) and delta is N(d1). On a 0.331 delta UBER call the true figure was 29.3 percent, an overstatement of 3.8 points, and the gap widens with volatility and time.
What is probability of touch?
The chance the stock reaches your strike at any point before expiry rather than finishing there. For an out-of-the-money strike it runs at roughly double the probability of finishing in the money, so a 29 percent contract gets tested about 59 percent of the time.
Does a 0.30 delta option really expire worthless 70 percent of the time?
Approximately, and the model actually gives slightly better odds than delta suggests for a short. What the rule of thumb hides is that the same position is likely to trade against you at some point first.
Why is the probability different for puts at the same delta?
Because of skew. Downside strikes trade at higher implied volatility, so the market is pricing a fatter left tail than the lognormal model behind your delta assumes. Treat a put delta as a lower bound on the chance of being tested.
Sources
Rules and thresholds above were checked against these documents on August 4, 2026. Exchange and broker rules change. Confirm anything you are about to act on with your own broker.
Keep reading
Do the math on your own trade
Every price in this article is an illustrative worked example, not a quote. Read The Greeks for the rest of the series, and the disclaimer before you act on any of it. Selling options carries real risk of loss, and the loss can be far larger than the premium you collected.